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COMPUTACIÓN E INFORMÁTICA ReCIBE, Año 4 No. 2, Mayo 2015
The machine learning in the prediction of elections
M.S.C. José A. León-Borges
Universidad Politécnica de Quintana Roo
M.A. Roger-Ismael-Noh-Balam
Instituto Tecnológico de Chetumal
Lic. Lino Rangel Gómez
Instituto Tecnológico de Chetumal
Br. Michael Philip Strand
Instituto Tecnológico de Chetumal,
Estudiante de Ingeniería en Sistemas Computacionales
Abstract: This research article, presents an analysis and a comparison of three
different algorithms: A.- Grouping method K-means, B.-Expectation a
convergence criteria, EM and C.- Methodology for classification LAMDA, using
two software of classification Weka and SALSA, as an aid for the prediction of
future elections in the state of Quintana Roo. When working with electoral data,
these are classified in a qualitative and quantitative way, by such virtue at the
end of this article you will have the elements necessary to decide, which
software, has better performance for such learning of classification.
The main reason for the development of this work, is to demonstrate the
efficiency of algorithms, with different data types. At the end, it may be decided,
the algorithm with the better performance in data management.
Keywords: Automatic Learning, fuzzy logic, grouping, Weka, SALSA, LAMDA,
state elections, prediction.
El aprendizaje automático en la predicción de las
elecciones
Resúmen: Este artículo de investigación presenta el análisis y comparación de
tres algoritmos diferentes: A.- método de agrupamiento K-media, B.-
expectativa de criterios de convergencia y C.- metodología de clasificación
LAMDA usando dos softwares de clasificación, Weka y SALSA, como auxiliares
para la predicción de las futuras elecciones en el estado de Quintana Roo.
Cuando se trabaja con datos electorales, éstos son clasificados en forma
cualitativa y cuantitativa, de tal virtud que al final de este artículo tendrá los
elementos necesarios para decidir que software tiene un mejor desempeño
para el aprendizaje de dicha clasificación. La principal razón para hacer este
trabajo es demostrar la eficiencia de los algoritmos con diferentes tipos de
datos. Al final se podrá decidir sobre el algoritmo con mejor desempeño para
el manejo de información.
Palabras clave: aprendizaje automático, lógica fuzzy, agrupamiento, Weka,
SALSA, LAMDA, elecciones estatales, predicción.
1. Introduction
The fascination for predict the future, is one of the intents and desires that man
still insists on getting. Much effort have individuals and companies to predict
various aspects, for example, climate and product prices in the market. For
example: Toro (2006) Forecast stock market using intelligent techniques,
Matamoros (2006) Methodology for predicting oil prices based on fractal
dynamics and Weron (2007) Modeling and forecasting electricity loads and
prices: A statistical approach. Other works are to: Matamoros (2005)
Methodology oil price prediction based on fractal dynamics; calculated
logarithmic returns, tracing methods, average values in time series to generate
probabilistic scenarios.
There are many works prediction Data mining, a variant is research on the
prediction and treatment of disease, alcohol use in adolescents, Vega (2009)
Data Mining Applied to Prediction and Treatment of Diseases. Another
perspective is: Jungherr (2012) Why the pirate party won the German election of
2009 or the trouble with predictions. A response to Tumasjan, A, Sprenger, TO,
Sander, PG, & Welpe, IM predicting elections with Twitter : What reveal 140
characters reveal political sentiment.
There are studies on predicting elections that have been made in countries such
as:
Spain, where Dellte (2012) Conducted prediction political tendency Twitter:
Andalusian elections 2012; For Holland, Tumasjan (2010), Predicting Elections
with Twitter. What about 140 Characters Reveal Political Sentiment; Germany,
Sang (2012) Predicting the 2011 senate election results with Dutch twitter. In
Proceedings of the Workshop on Semantic Analysis in Social Media. Jungherr
(2012) Why the pirate party won the German election of 2009 or the trouble with
predictions: A response to Tumasjan, A, Sprenger, TO, Sander, PG, & Welpe,
IM "predicting elections with Twitter. What reveal 140 characters about political
sentiment "; and Canada, where Sidorov (2013) did an Empirical study of
machine learning based approach for mining review in tweets. In Advances in
Artificial Intelligence.
According to (Becerra-Fernandez, 2003), the discovery of knowledge in
databases has made the computational procedures in automatic programming
are increasingly sophisticated. Say Berry (1997), the data mining aims to uncover
patterns and relationships to make predictions.
First, the classification of the data, by a process of unsupervised learning as the
grouping clustering, brings the find of groups that are different but the individuals
are equal among themselves as noted (Vega, 2012) In the methodology of data
mining.
We select the use of the data mining software called Weka, because it is an easy
tool, and where different jobs are chose: like, Empirical studies of machine
learning based approach for opinion mining in tweets, (Sidorov, 2013), The
comparison of different classification techniques using Weka for breast cancer
(Bin, 2007) and the compared in Data Mining Applied to Prediction and Treatment
of Diseases (Vega, 2012) and the different software products for data mining.
Also we chose a hybrid model, see table 1, as clustering techniques for better
results, some work related are, for example: The Data Mining applied to
prediction and treatment of diseases (Arango, 2013) and Methods for predicting
stock market indices. Echoes of Economics, (García, 2013).
Table 1.Description of prediction models (Garcia, 2013) and (Arango, 2013).
Technique Model type
Multiple Regression Linear
Neural networks (Radial Basis Function, RBF and Backpropagation)
Nonlinear
Methods K-nearest neighbor Nonlínear
Probabilistic neural network (PNN) Nonlínear
Genetic algorithm Nonlinear
Neuro-fuzzy networks Nonlinear e Hybrid
Neural networks MPL Nonlinear
Table 1.Description of prediction models (Garcia, 2013) and (Arango, 2013).
Technique Model type
SVM support vector machine Nonlinear
With comparative purposes, this work shows the results of the classification
performed into two applications of software: Weka and SALSA, with different
techniques of clustering. Also are shown and detailed the experiment on the
preparation of the data. In the first part it explains our intention of predicting state
elections with qualitative and quantitative data as well as briefly describing of the
three techniques of clustering: Expectation-Maximization, k-means and describe
the methodology of classification LAMDA. Was made, a comparison of the
techniques and software used with the results obtained, finally, we show the
performance of each software tool.
2. Background
2.1 References
To analyze the decision-making of the citizens, it is necessary to have
instruments of measurement with respect to its electoral behavior, such as
surveys and projections. In Mexico in the first part there is something written, but
on the second there is very little.
The literature on electoral projections is basic, because studies should nourish it,
as in the case of statistical analysis, which are scarce (Torres, 2000). The lack of
specialized bibliography, is due to the fact that since 1993, are disseminated by
the Federal Electoral Institute IFE, and the state electoral bodies, the overall
results and with some levels of disaggregation; what has meant is that there are
no historical series of voting, nor criteria to build units of comparison.
With the practice, of presenting the basic statistics disaggregated to the level of
electoral section and even casilla, have been ameliorated some of the described
shortcomings, however, there remains the need to analyze and interpret the data;
setting criteria for the construction and use of statistical aggregates; and finally,
to make attempts of predictions.
The literature on individual electoral behavior, has underlined the existence of
stable predispositions to vote, sustained in the long term, on the basis of which
the decision be finalized, except that they act on the individual circumstances of
a particular choice: candidates, issues, and so on, all forces of short-term.
2.2 Prediction of state elections
The prediction of the 2009 elections in Germany, using the techniques
referenced, as shown in (Jungherr, 2012) Why the party won the German election
of 2009 or the trouble with predictions: was done by taking into account the
frequency of mentions and to get the total mentions, replication of mentions and
percentages of mentions. The sample is less than a month, and takes
representative days. It also takes into account the progression of the followers.
The analysis of the results is quantitative.
On the other hand, the classification in the Empirical study of machine learning
is based in approach for opinion mining in tweets. Sidorov (2013), through
automatic learning, shows the possible classifications of classes and Support
Vector Machine SVM as the best binder driving records 3393 as the best data
set of training.
In this case, we take the elections in the state of Quintana Roo in the years 1998,
2004 and 2010.
3. Theoretical framework
3.1 Automatic learning
Today’s Data Mining can be defined in terms of three easy concepts:
Statistics with emphasis on exploratory data analysis proper, big data and
machine learning.
Samuel (1959) say, the definition of machine learning, was given to the field of
study that assigns to the computers the ability to learn without being explicitly
programmed. In other words, machine learning investigates ways in which the
computer can acquire knowledge directly from data and thus learn to solve
problems. The automatic learning is the acquisition of new knowledge, the
development of a motor and cognitive skills through instruction or practice, the
organization of new knowledge, effective representation and discovery of new
facts and theories through observation and experimentation. The types of
knowledge acquired are parameters in algebraic expressions, decision trees,
formal grammar, production rules, logic-based formal expressions, graphs and
networks, frameworks and diagrams and other procedural encodings and
computer programs.
This learning is applied to many areas such as chemistry, education, computer
programming, expert systems, video games, mathematics, music, natural
language processing, robotics, speech recognition and image, and sequences of
prediction example: An overview of machine learning, in Machine learning, by
(Carbonell, 1983) among others.
3.2 Techniques of grouping or clustering
The Clustering techniques, is referred in English as grouping, are procedures
which are used to group a series of items. Clustering is used in statistics and
science. The methods to deal with are: the hierarchical method because it is an
exploratory tool designed to reveal the natural groups within a set of data that
would otherwise is not clear. It is useful when you want to group a small number
of objects, may be cases or variables, depending on if you want to classify cases
or examine relationships between the variables.
A review of clustering algorithms, can be referenced by (Xu, 2005) and discuss
different algorithm. The hierarchical method is built by a cluster of trees or
hierarchical clusters. Each node contains clusters children. Categorized in
agglomerative and divisive. The first begins with a cluster and after two or more
similar clusters. The second begins with a cluster containing all the data points
and recursively divides the group most appropriate. The process continues and
stops until the criterion is improved.
Table 2.Classification of clustering algorithms (Berkhin, 2006).
Method Category
Hierarchical method Agglomerative algorithms y divisive algorithms
Method partition and relocation
Clustering probabilistic, K-mediods y K-means.
Partitioning method based on density
Clustering connectivity clustering based on density and density functions.
Network-based method
Based on co-occurrence of categorical data Method
Other clustering techniques
Constraint-based clustering, graph-partitioning, clustering algorithms with supervised learning and clustering algorithms with machine learning
Scalable clustering algorithms
Algorithms for high dimensional data
Subspace clustering and co-clustering techniques
3.1.1 K-means
K-means (MacQueen, 1967) is one of the simplest unsupervised learning
algorithms that solve the well known clustering problem. k-means is one of the
simplest unsupervised learning algorithms that solve the well known clustering
problem. This algorithm is classified, as a method of partitioning, and relocation
of each of its clusters, represents the average of their points centroid. The
advantage of using this is by the quick view graph and statistics. The target
function, is the sum of the errors between the centroid and their points, i.e. the
total variance within the cluster.
Although it can be proved that the procedure will always terminate, the k-means
algorithm does not necessarily find the most optimal configuration, corresponding
to the global objective function minimum. The algorithm is also significantly
sensitive to the initial randomly selected cluster centres. The k-means algorithm
can be run multiple times to reduce this effect. K-means is a simple algorithm that
has been adapted to many problem domains, it is a good candidate for extension
to work with fuzzy feature vectors.
Finally, this algorithm aims at minimizing an objective function, in this case a
squared error function.
3.1.2 Expectation Maximization EM
The algorithm of Expectation Maximization, EM, belongs to the family of finite
mixture models, used for segmenting multivariable data. It is a probabilistic
clustering algorithm, where it seeks to know the target function of the unknown
probability to which the data set belongs. Each cluster is defined by a normal
distribution, the problem is, that the distribution is not known to which the data
and parameters corresponds. Specifically, the algorithm is divided into two
stages: expectation and a convergence criteria.
The first with unknown underlying variables, using parameter estimation up to the
observation. The second provides a new estimation of the parameters, as shown
in the papers: The algorithm of expectation-maximization (Moon, 1996) and
unsupervised learning of finite mixture models (Figueiredo, 2002). Iterate both,
until converge. In other words, the calculation of the probabilities or the expected
values is performed and the value of the parameters of the distributions, is
calculated for maximizing the probability of distributions of the data. The
estimation of the parameters is considered to be the probability that the data
belongs or does not belong to a cluster.
3.1.3 Fuzzy Logic
The fuzzy logic deals when imprecise or subjective terms is handled, where an
element can belong to multiple sets of partial form. Fuzzy logic was defined in
this work by membership functions of campaign by the functions mean and
standard deviation.
The characteristic function μs commonly used to define if a member belongs or
not to a member, or a set of members (S), μS(x) = 1, if x is a member of S and
μS(x) = 0, if x is not a member of S.
Formula 1. Feature.
The operations to be performed on fuzzy sets are shown in table 3.
Table 3.Operations on fuzzy sets.
Operation
Inclusion or subassembly
Union. Zadeh logical OR operator (max)
Intersection. Zadeh logical AND operator (min)
Denial or supplement
Cartesian product
Table 3.Operations on fuzzy sets.
Operation
Cartesian co-product
3.1.4 LAMDA classification methodology
The LAMDA algorithm, Learning Algorithm for Multivariate Data Analysis, is a
classification method developed by N. Piera and J. Aguilar (Aguilar, 1982),
(Desroches, 1987), (Piera, 1989). It is created by a principle to categorize data,
where there may be many variables, however, classified in both numeric and
symbolic, quantitative data and qualitative data.
LAMDA enters the classification within the theory of networks of radial basis
function, which is a method to improve the generalization of new data. The
learning of radial basis can be given supervised or not supervised. Supervised,
when it seeks to minimize the error between the output value of the network and
the desired output value, using least squares. Non-supervised, where it allows to
divide the space of input patterns into classes. The number of classes, is the
number of hidden neurons in a radial basis network.
An object X, is represented by a vector that contains a set of features, in this case
it can be the votes of party1, party 2 or party 3, called descriptors. In the
classification, each object X is assigned to a class. A class is defined as the
universe of descriptors that is characterized as a set of objects.
LAMDA, performs classification according to criteria of similarity in two stages:
first, the similarity criteria of each descriptor object corresponding, to the
descriptor of a given class measured, this is also known as the obtaining or
calculation of the degree of marginal adequacy MAD (Marginal Adecuation
Degree). Second, when the measurement of the relevance of an object is added
to a particular class, this is also known, as the obtaining or calculation of the
degree of overall adequacy GAD (Global Adecuation Degree).
The calculation of GAD, deals with the concept of diffuse connective, which is
explained by the aggregation function as linear interpolation of t-norm with t-
conorma. The total diffuse intersection and the total diffuse union respectively.
These aggregation operators get the GAD an individual data added to a class.
The connectors used in GAD are, the intersection, t-norm and union, t-conorma.
The role of aggregation (Piera and Aguilar, 1991) is a linear interpolation between
t-norm () and t-conorma (rβ ).
Finally the global maximum of similarity of an object in a class allows the definition
of a class that best describes the object.
In other words MAD is a related term of how similar a descriptor object is, to the
same descriptor of a given class and GAD is defined as the degree of relevance
of an object at a given class given, as a function of relevance diffuse.
Where:
ρ(c,d)=Learning Parameter (Rho) for class c and the descriptor d.
X(i,d)=The Descriptor d of object i.
The implementation of LAMDA, includes a probability function for estimating the
distribution of descriptors based on fuzzification, the process of converting an
element in a value of each class to which it belongs.
The main features and that makes difference of LAMDA are the NIC, Not
Information Classified, which allows you to perform supervised classifications
and non-supervised, learning functions are based on arithmetic, they can modify
the parameters representative of each class. NIC accepts all objects contained
in the universe of description with the same degree of appreciation GAD. For
more information about the learning algorithm for the analysis of multivariate
data, refer (Aguado-Chao, 1998), a mixed qualitative quantitative self-learning
classification technique applied to situation assessment in industrial process
control.
4. Methodology
It is important to study the relationship between the historical trend of the vote
and the electoral results of a specific process; it is important because it allows us
to make predictions, which can, in good measure, sensitizing political actors and
citizens about the possible results of the electoral process.
It is pertinent to note, that the research was carried out, by ordering the results
of the processes of local governor 1998, 2004 and 2010 of the state of Quintana
Roo, to develop historical series of votes, which were necessary to carry out the
projections.
The election results are not entirely accidental events, fully relieved by past
events, and that much of what happens in local processes allows us to
contemplate the possible scenarios of the local process.
Thus, in the case of the local executive, it incorporates data from the last three
elections for governor 1998, 2004 and 2010, data were analyzed from municipal
presidents and local deputies, the above are for every 3 years; due to the
difficulties to normalize the data and the lack of the data themselves; it was
determined to use the data for governorship.
The historical evolutions that have had the political parties in the State of
Quintana Roo, clearly shows how diversity have emerged from these political
actors , but with the passage of time it have been terminated. The political parties
which, with the passage of time have subsisted alone or coalitions are: the PAN,
PRI and the PRD, for the case study.
To obtain the data already standardized, was made a historical analysis of the
evolution of political parties and their coalitions; it concluded: in the case of the
state of Quintana Roo, in all elections for governor all three major political parties
in Mexico were present or were coalitions.
First, and for not having bias or trend, it was taken, in the order they appear
registered in the State electoral unit, in such a way that they appear in the
following way: PAN, PRI and PRD or their respective coalitions. In that sense we
started to take the year of election 1998, 2004 and 2010 as data, being the data
that was obtained from State Electoral Body and taking into account that the
major election is performed every 6 years.
The data are then classified by electoral district of the years: 1998, 2004 and
2010 for these years there have been 15 districts; in such a way that the division
was carried out by electoral district and for each electoral district it disaggregated
by casilla, for every casilla there was a need to standardize the information; for
each casilla is divided by type of casilla, in such a way that it was the unbundling
of the most basic data form.
The record is as follows: year of the election, the electoral district, casilla, political
1, political 2 and 3. Leaving 2 types of data: qualitative data and the others
quantitative.
5. Experiments
5.1 Salsa
The generated file of the data, must include the header, a, according to the format
that handles the tool for this case SALSA, subsequently the data is standardized;
file, b, is saved. It is appropriate to perform the loading of the data through the
file in text format, c.
Once it has been proceeded to load the data in SALSA, ii proceeds to process
them d.
5.1.1 File Header
The format of the header of the file that will be used to process the data in the
tool is the one shown in table 4, the tool asks that at the beginning of the file
exists & and the other columns should be separated by a Tab.
Table 4.File header.
&ANIO DIST CAS PAN PRI PRD
.
5.1.2 Standardized Data year 1998- 2010
The data were grouped by years 1998, 2004 and 2010, the electoral district to
which corresponds I. XV, the number and type of polling station Basic,
contiguous, special or extraordinary and finally the vote for the party.
Table 5.SALSA dataset file.
&ANIO DIST CAS PAN PRI PRD
1998 I 300B 83 149 45
...
1998 XV 297B 11 235 236
Table 5.SALSA dataset file.
&ANIO DIST CAS PAN PRI PRD
...
2004 I 300B 206 161 20
...
2004 XV 297B 3 35 127
2010 I 300B 47 153 58
...
2010 XV 297B 73 137 79
5.1.3 Data loaded
In figure 1, it is seen as if the tool has already grouped and sorted all 100 % the
data, in a quantitative and qualitative manner, if we are to observe the previous
point, the file is a set of unsorted and unclassified data, where there are numbers
and alphanumeric.
Figura 1. Details of descriptors.
5.1.4 Processed data
The historical data processed contain 3390 samples and 15 descriptors or
physical variables obtained by the normalization done to the election data.
Through a standardization of data, it shows the representation of the behavior of
the variables. The minimum and maximum values that are used in each
descriptor helps homogenize the influence of its dimensions.
Figura 2. Profiles.
As a last step the profile of the class e is obtained.
5.1.5 Descriptors
This context has 6 descriptors with the current state of the active descriptor:
Table 6.Descriptors of the dataset.
No. Nombre Tipo Max Min
1 Anio CUANTITATIVO 2010 1998
2 DIST CUALITATIVO
Label no. 1 …. Label no. 15
Valor I …. Valor XV
3 CASILLA CUANTITATIVO 741 1
4 PAN CUANTITATIVO 248 0
5 PRI CUANTITATIVO 491 0
6 PRD CUANTITATIVO 491 0
5.2 WEKA
A procedure is performed similar to that made with salsa. As a first step it
generates a data file, the file generated from the data, must include the header
a, according to the format the tool handles, for this case Weka , after such data
is standardized, the file is saved. It is appropriate to perform the loading of the
data through the file in text format b.
5.2.1 File Header
In the case of the EM algorithms and K-means using the software Weka, the
attribute polling station had to be removed, due to both grouping classifiers does
not allow qualitative data.
Figura 3. File Weka Dataset.
5.2.2 Data loaded
It is noted how Weka does the classification in the form of a table and in the form
of bars, in the case of the table it makes a classification by district and the result
of the grouping of the data for each district. For the graphs it only shows its
concentration and one would have to deduce that each bar is an electoral district.
Figura 4. Classification.
5.2.3 Data processed by K-means
As how it can be observed in the circles in Figure 3, the tool generates two Cluster
Centroids turns the display XI and XIII and it handles them as if they were the
most distant and from that first the adjustment is made.
Figura 5. Cluster Model - K-means.
Figura 6. Cluster Plot.
Generation of results through the Weka methods.
6. Advantage
Proper use of data classification algorithms, has several advantages. With this
work, we have concluded that there are the following advantages:
In an investigation of qualitative nature, these algorithms serve to validate the
data, because they are based on mathematical models. Once the system has
been trained, within the domain that is done, the manipulation of data,
interpretation of the results is often simple. Because, using the mathematical
methods, experiments can be repeated and provide the same results for
verification.
The clustering techniques, have significant advantages in terms of time. The
quality of the results depends on the similarity measure used. Further the quality
is measured by its ability to discover hidden patterns.
The cost of learning is null. No need to make any assumptions about the concepts
to learn. You learn complex concepts using simple functions such as local
approximations. You can extend the mechanism to predict continuous values.
7. Results and future work
Although Weka is a software that allows you to make automated classifications
by different methods and forms, in this analysis only the methods proposed at
the beginning of the article were used, in such a way that it shows, the results
that were more adjusted or approximated the classifications long awaited by the
expert. This is due to the fact that there are qualitative data, not all of the tools
have the ability to properly classify and on the other hand the behavior cannot be
explained under some statistical method. The software that best made the
classifications was SALSA, see section 5.1, C and D, due to the fact that it
included in the right way, the qualitative data along with the quantitative data.
With the data that has already been processed in both Weka and in SALSA, an
analysis and comparison was carried out. The analysis was performed with
respect to its performance to the clustering of quantitative and qualitative data,
on the other hand, is made with respect to the efficiency when performing such
data. In this point, it can be seen that the 3393 data 100 %, were classified
properly in SALSA, unlike Weka which could not reach its classification in this
same percentage.
The application of these algorithms in state elections is very efficient. The
algorithms to predict the future, can be used in real time, like an option for the
process electoral. It would be very useful and efficient to determine trends in state
election by electoral districts in real time. For this case it is very useful to use the
larger districts. With the bases shown in this work, on the future, a forecast can
be done for any mathematical methodology as well as the correlations between
the data of the districts and the casillas, and completing the corresponding
analyzes by experts; for the work or the purposes to be used. The application of
these algorithms in state elections is very efficient. The algorithms to predict the
future, can be used in real time, like an option for the process electoral. It would
be very useful and efficient to determine trends in state election by electoral
districts in real time. For this case it is very useful to use the larger districts.
Based on the article and with the base shown in this work, in the future, you can
make projections for a forecast, to be classified with new data and clustering
algorithms; and we will make an analysis, a correlations between the data of the
districts and the casillas. Our work will be done, for the purposes that the political
groups consider relevant.
8. Conclusions
This article, find the current state of the art, related to the prediction of elections,
using automatic programming. In particular of three algorithms: A.- Grouping
method K-Means, B.- EM and C.- Methodology for classification LAMDA, through
the use and application of the Weka and SALSA, as support tools for the
processing of standardized set of data, to make electoral predictions, for the
election of governor in the state of Quintana Roo. Due to the set of data that were
analyzed qualitative and quantitative as a whole, it was determined that the
algorithm of LAMDA that used implicitly the SALSA software is the one that best
returned the results, and is adjusted to the criteria of a more accurate form.
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Notas biográficas:
José Antonio León Borges 2014: Candidato a Doctor en Sistemas
Computacionales: Universidad del Sur, plantel CanCùn 2012. Maestría en
Ciencias de la Informática. Universidad Villa Rica. Boca del Río, Veracruz. 2010.
Especialidad en Base de Datos. Universidad Villa Rica. Boca del Río, Veracruz.
2009. Licenciatura en Computación y Sistemas. Universidad Villa Rica. Boca del
Río, Veracruz. Inglés: 453 puntos en TOEFL Perfil Deseable Dic 2014-Dic 2017
Roger Ismael Noh Balam 2014: Candidato a Doctor en Sistemas
Computacionales: Universidad del Sur, plantel CanCùn 2000. Maestría en
Administración. Instituto de Estudios Universitarios, plantel CanCún 1994.
Licenciatura en Informática. Instituto Tecnológico de Chetumal 1994-2003:
Profesor de Tiempo Completo Instituto Tecnológico de Chetumal 2003-2012:
Titular de la Unidad Técnica de Informática y Estadística Instituto Electoral de
Quintana Roo 2012: Profesor de Tiempo Completo Instituto Tecnológico de
Chetumal
Lino Rangel Gómez 2008: Maestría en Tecnología Educativa Universidad Da
Vinci 1993: Licenciado en Computación Universidad Autónoma del Estado de
Hidalgo. 2002:Subdirector de Planeación del Instituto Tecnológico de Chetumal
Micheal Philip Strand 2015: Instituto Tecnológico de Chetumal, Estudiante de
la Ingeniería en Sistemas Computacionales 2012: University of Belize,
Architectural Technology, Associates degree in Applied Science
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